Complexbandsk(E)inasemiconductorcrystal,alongageneraldirectionn,canbecomputedbycastingSchrodinger’sequationasageneralizedpolynomialeigenvalueproblem.Whenworkingwithprimitivelatticevectors,theorderofthiseigenvalueproblemcangrowlargeforarbitraryn.Itis,however,possibletoalwayschooseasetofnon-primitivelatticevectorssuchthattheeigenvalueproblemisrestrictedtobequadratic.ThecomplexbandssoobtainedneedtobeunfoldedontotheprimitiveBrillouinzone.Wehavedeveloped[JPCM_2012]aunifiedmethodtounfoldrealandcomplexbands.Thismethodensuresthatthemeasure associated
with the projections of the non-primary wavefunction onto all
candidate primary wavefunctions is invariant with respect to the
energy E.

We
have also computed [IWPSD_2011] the orientation dependent complex
bandstructure of InSb, InAs, GaSb, InP and GaAs, and the orientation
dependent probability of band to band tunneling in these materials.
These direct bandgap III-V materials are attractive candidates for
Tunnel FETs. Comparison of our results with Kane’s two-band model
commonly used in TCAD simulation, demonstrates the inaccuracies of
the latter. Our results will be useful in the design of better
performing Tunnel FETs in these materials.

Band to band tunneling in heterojunctions

TCAD tools must be able to handle BTBT through heterojunctions, since
for example, an appropriately designed heterojunction can boost
on-current significantly in Tunnel FETs. It is known that a
multiscale approach which captures the complex bandstructure within
the bandgap is critical to reliably predict BTBT current through
homojunctions. Evanescent states in heterojunctions depend on both
materials forming the junction. However, semi-classical schemes to
handle BTBT through heterojunctions simply follow a region based
approach, stitching together the complex bands of the two materials.
The accuracy of computing BTBT current using this idea is not known.
We have compared [IWCE_2012] this semi-classical approach against the
results of an accurate quantum computation.

Multiscale Modeling of phonon assisted band-to-band tunneling

We have developed [JAP_2013] a TCAD compatible multiscale model of phonon-assisted band-to-band tunneling in semiconductors, which incorporates the non-parabolic nature of complex bands within the bandgap of the material. This model is shown capture the measured current-voltage data in silicon, for current transport along the [100], [110], and [111] directions. Our model will be useful to predict band-to-band tunneling phenomena to quantify on and off currents in tunnel FETs and in small geometry MOSFETs and FINFETs.